Length spectra and degeneration of flat metrics

• 成果类型: Article
• 署名作者: Duchin, Moon; Leininger, Christopher J.; Rafi, Kasra
• 署名单位: University of Michigan System; University of Michigan; University of Illinois System; University of Illinois Urbana-Champaign; University of Oklahoma System; University of Oklahoma - Norman
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-010-0262-y
• 发表日期: 2010
• 页码: 231-277
• 关键词: teichmuller space; SURFACES; geodesics; RIGIDITY; geometry

摘要

In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectrally rigid, that is, when the length vector determines a metric among the class of flat metrics. Secondly, we give an embedding into the space of geodesic currents and use this to obtain a compactification for the space of flat metrics. The geometric interpretation is that flat metrics degenerate to mixed structures on the surface: part flat metric and part measured foliation.